Weak field equations and generalized FRW cosmology on the tangent Lorentz bundle

Abstract

We study field equations for a weak anisotropic model on the tangent Lorentz bundle TM of a spacetime manifold. A geometrical extension of General Relativity (GR) is considered by introducing the concept of local anisotropy, i.e. a direct dependence of geometrical quantities on observer 4−velocity. In this approach, we consider a metric on TM as the sum of an h-Riemannian metric structure and a weak anisotropic perturbation, field equations with extra terms are obtained for this model. As well, extended Raychaudhuri equations are studied in the framework of Finsler-like extensions. Canonical momentum and mass-shell equation are also generalized in relation to their GR counterparts. Quantization of the mass-shell equation leads to a generalization of the Klein-Gordon equation and dispersion relation for a scalar field. In this model the accelerated expansion of the universe can be attributed to the geometry itself. A cosmological bounce is modeled with the introduction of an anisotropic scalar field. Also, the electromagnetic field equations are directly incorporated in this framework.

On the Analyticity of Static Solutions of a Field Equation in Finsler Gravity

“…the horizontal Laplacian of F, see [52], Remark 5. From this point of view, it might be interesting to analyse a generalization of the Einstein field equations on the whole tangent bundle of the spacetime, obtained recently [53], based on Sasaki type metrics and nonlinear connections on it.…”

Dynamics in varying vacuum Finsler–Randers cosmology

“…The derived field equations are more general than the Riemannian ones [32]. These equations can also be derived in the case of the Finsler-Randers model by making further assumptions [33]. Indicative works in the Finsler-Randers model are [24,[34][35][36][37][38][39][40].…”

Bounce Cosmology in Generalized Modified Gravities

“…Extremization of the total action S TM with respect to the metric components g µν and v αβ leads to the following field equations [51]:…”

“…. Applying these field equations in the FRW metric (1), focusing on the flat case, and assuming the usual matter perfect fluid (12), one obtains the following modified Friedmann equations [51]:…”